The graph of each function and the inverse is attached
How to find the inverse of the function
The inverse of the function is calculated by making x the subject of formula and interchanging the variables. This is done as as follows
A. g(x) = 2x-1
let y = g(x)
y = 2x - 1
2x = y + 1
x = (y + 1) / 2
interchanging the variables
y = (x + 1) / 2.
The inverse of g(x) = 2x-1 is g⁻¹(x) = (x + 1) / 2.
B. f(x) = 2/3 x + 2
let y = f(x)
y = 2/3 x + 2
(y - 2) = 2/3 x
x = 3/2 (y - 2)
interchanging the variables
y = 3/2 (x - 2)
The inverse of f(x) = 2/3 x + 2 is f⁻¹(x) = 3/2 (x - 2)